an:06102471
Zbl 1387.58037
Bergamasco, A. P.; Mendoza, G. A.; Zani, S.
On global hypoellipticity
EN
Commun. Partial Differ. Equations 37, No. 9, 1517-1527 (2012).
00308644
2012
j
58J99 35H10 35B65 35F05 57R22
global hypoellipticity; global solvability; line bundles
Summary: We consider a first order linear partial differential operator of principal type on a closed connected orientable two-dimensional manifold sending sections of one complex line bundle to sections of another. We prove that the assumption of global hypoellipticity of the operator implies a relation between the degrees of the line bundles and the Euler characteristic of the manifold.